Solve 2x-5x^22x-3)

$$2 x - 5 x ^ { 2 } 2 x - 3 )$$

Evaluate

$$-10x^{3}+2x-3$$

Solution Steps

To multiply powers of the same base, add their exponents. Add 2 and 1 to get 3.

$$2x-5x^{3}\times 2-3$$

Multiply 5 and 2 to get 10.

$$2x-10x^{3}-3$$

Differentiate w.r.t. x

$$2-30x^{2}$$

Steps Using Derivative Rule for Sum

The derivative of a polynomial is the sum of the derivatives of its terms. The derivative of a constant term is 0. The derivative of ax^{n} is nax^{n-1}.

$$2x^{1-1}+2\left(-10x\right)x^{2-1}$$

Subtract 1 from 1.

$$2x^{0}+2\left(-10x\right)x^{2-1}$$

Multiply 2 times -5\times 2x.

$$2x^{0}+\left(-20x\right)x^{2-1}$$

Subtract 1 from 2.

$$2x^{0}+\left(-20x\right)x^{1}$$

For any term t, t^{1}=t.

$$2x^{0}+\left(-20x\right)x$$

For any term t except 0, t^{0}=1.

$$2\times 1+\left(-20x\right)x$$

For any term t, t\times 1=t and 1t=t.

$$2+\left(-20x\right)x$$